The present invention relates to a method for evaluating the life of a connection, and more particularly to a method for evaluating the life of a connection which greatly depends on thermal fatigue, such as a solder connection of an electronic circuit device.
With respect to general fatigue life of metal, several methods for evaluating it and life rules therefor, as shown in Table 1, have been proposed on the basis of research and experience of fatigue breakdown accidents. Some of the methods have been put into practice.
Particularly, it is known that the Manson-Coffin rule shown as No. 1 in the table can be used to evaluate the low cycle fatigue life of many metals. The actual life can be evaluated by the Repetition Amendment Speed Equation No. 9 in the table which is obtained by modifying this rule regarding the repetitive frequency f of fatigue and the length a of a crack.
Further, a method for evaluating the life of the solder connection of an electronic circuit device is disclosed in Solid State Technology July (1970) pp. 48-54.
TABLE 1 __________________________________________________________________________ LIFE EQUATION OR CRACK No. DEVELOPER ADVANCING SPEED EQUATION __________________________________________________________________________ 1 S. S. Manson, .DELTA..epsilon..sub.p .multidot. N.sup.n = C L. F. Coffin (Manson-Coffin RULE) 2 S. S. Manson, .SIGMA..PHI..sub.f = 1 G. R. Halford .PHI..sub.f = 1/N.sub.pp + 1/N.sub.cc + 1/N.sub.cp + 1/N.sub.pc (STRAIN REGION .DELTA..epsilon..sub.pp /D.sub.p = 0.75 N .sub.pp .sup.-0.6 DIVISION TECHNIQUE) .DELTA..epsilon..sub.pp /D.sub.p = 0.75 N .sub.pp .sup.-0.8 .DELTA..epsilon..sub.pp /D.sub.p = 1.25 N .sub.pp .sup.-0.8 .DELTA..epsilon..sub.pp /D.sub.p = 0.25 N .sub.pp .sup.-0.8 3 H. W. Liu d.sub.a /d.sub.N = C(.DELTA..sigma.).sup.2 a .DELTA..sigma. = .sigma.max-.sigma.min 4 P. C. Paris d.sub.a /d.sub.N = C(.DELTA.K).sup.n (Paris RULE) .DELTA.K = Kman-Kmin 5 G. Welter, d.sub.a /d.sub.N = (C.epsilon..sub.TR .sqroot.a) J. A. Choquet .epsilon..sub.TR = .epsilon..sub.p + .epsilon..sub.e 6 T. Yokobori d.sub.a /d.sub.N = Cf.sup.m .DELTA.K.sup.n exp(-Q/kT) (KINETICS MODEL OF DISLOCATION) 7 W. Elber d.sub.a /d.sub.N = C(.DELTA.Keff).sup.n (RULE OF COEFFICIENT .DELTA.Keff = Kmax-Kop ENLARGING EFFECTIVE STRESS) 8 J. R. Rice, d.sub.a /d.sub.N = C(.DELTA.J).sup.n P. C. Paris 9 H. D. Solomon, d.sub.a /d.sub.N = Ca(.DELTA..epsilon..sub.p).sup.nfm L. F. Coffin (REPETITION AMEND- MENT SPEED RULE) 10 K. Tanaka, S. Taira d.sub.a /d.sub.N = C(.DELTA..PHI.).sup.n __________________________________________________________________________
(N; LIFE), .DELTA..epsilon.p; PLASTIC STRAIN AMPLITUDE), (C, n, m; CONSTANT), (N.sub.pp, p p WAVEFORM LIFE), (N.sub.cc ; c c WAVEFORM LIFE), (N.sub.cp ; c p WAVEFORM LIFE), (N.sub.pc ; p c WAVEFORM LIFE), (D.sub.p ; PULLING FRACTURE DUCTILITY AT A HIGH TEMPERATURE FOR SHORT TIME), (Dc; CREEP FRACTURE DUCTILITY), .DELTA..sigma.; STRESS RANGE), (.DELTA.K; RANGE OF COEFFICIENT ENLARGING STRESS), (a; CRACK LENGTH), (.DELTA..epsilon..sub.TR ; ENTIRE STRAIN RANGE), (.DELTA..epsilon..sub.p ; PLASTIC AND ELASTIC STRAIN RANGE), (f; REPETITION FREQUENCY), (Q; ACTIVATION ENERGY), (k; BOLTAMANN's CONSTANT), (T; TEMPERATURE), (.DELTA.Keff; RANGE OF COEFFICIENT ENLARGING EFFECTIVE STRESS), (Kop; K AT CRACK OPENING), (.DELTA.J; INTEGRATION RANGE), (.DELTA..PHI.; RANGE OF DISPLACEMENT OF CRACK OPENING)
To account for the influence of distortion amplitude on fatigue life, generally, the plastic distortion amplitude .DELTA..epsilon..sub.p in the life equations of Nos. 1 and 9 in Table 1 is adopted. .DELTA..epsilon..sub.p is defined as the range of distortion in the hysterisis stress-strain curve when mechanical stress is repeatedly applied to a material.
However, this .DELTA..epsilon..sub.p at a solder connection cannot be measured by the conventional techniques shown listed in Table 1. The reason therefor is as follows. If a temperature as high as the melting point of solder changes at e.g. a solder connection of a flip chip for an electronic circuit device, because of a difference between the flip chip and a substrate in their thermal expansion coefficient, the stress-strain occurring in the solder becomes a three-dimensional stress-strain state, and further changes because of the great dependency of the solder itself on temperature. In this way, the above conventional methods do not pay attention to the influences from a temperature cycle in estimating the range of distortion. For example, the junction between the flip chip for an electronic circuit and a substrate is subjected to great temperature change; its temperature will increase up to immediately below the melting point of solder (183-320.degree. C. in Pb-Sn series) because of heat generation in electronic components and environmental temperature. Nevertheless, the conventional techniques do not take such a temperature change in to account so that they cannot correctly evaluate the life of the junction subjected to the thermal fatigue. More specifically, the advancing speed of a crack at the connection depends on the shape of the connection. The above conventional techniques do not take this consideration; therefore, they cannot know the remaining sectional area so that they cannot design the weight resistance and current capacity of the connection. Particularly, the technique disclosed in the above reference Solid State Technology takes only shearing strain .gamma..sub.max into consideration but does not take temperature dependency of the stress-strain of the solder for this shearing strain. Therefore, this technique also cannot evaluate the life of the junction or connection subjected to thermal fatigue. Thus, the conventional life evaluation methods cannot correctly evaluate the life of the connection causing many poor quality products to be made.